Solve for $x$ : $2x^2 + 18x + 40 = 0$
Explanation: Dividing both sides by $2$ gives: $ x^2 + {9}x + {20} = 0 $ The coefficient on the $x$ term is $9$ and the constant term is $20$ , so we need to find two numbers that add up to $9$ and multiply to $20$ The two numbers $5$ and $4$ satisfy both conditions: $ {5} + {4} = {9} $ $ {5} \times {4} = {20} $ $(x + {5}) (x + {4}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x + 5) (x + 4) = 0$ $x + 5 = 0$ or $x + 4 = 0$ Thus, $x = -5$ and $x = -4$ are the solutions.